An extra finger in a human or animal would be polydactaly, and that kid's kid will probably have an extra finger too! Like silkies, it would be a trait usually passed on as dominant with the 5th toe. As for a whole leg though... that's something much bigger and I wonder if snipping it off would...
If it acts healthy and the leg doesn't put it at a disadvantage, it sure can be a pet, no problem if you have the time and space for it. I know some profs who have whole binders full of various types of birth defects.
I wouldn't be surprised if the age, the cold, or the parent stock all had a...